Abstract Students will use unit analysis to
calculate parts per million represented by given ratios
and determine in a given scenario whether local health
officials should close a lake that has been contaminated.
Purpose – Students will be able to calculate
ppm and use this number to make decisions concerning
health risks.

Objectives Students
will be able to:-

i. Calculate ppm and ppb by using unit analysis when
given a ratio of amounts
ii. Determine in ppm what constitutes a health risk
for a particular toxin given data

National Science Education StandardsMeasurementUnderstand measurable attributes of objects and the units,
systems, and processes of measurement
Apply appropriate techniques, tools, and formulas to
determine measurements

Have
the students present their representations of the concentration
of one part per million to the class. Allow time for
discussion of the representations. Make sure that you
do the dilution activity last and pass out the chart
from the Dilution Activity to the rest of the class.
Complete the chart with the rest of the class and have
the class answer the following questions:

2.
Which container has the highest mixing ratio? (# 1) Which
has the lowest mixing ratio?
(# 10)

3.
What happens to the color of the liquid as the mixing
ratio decreases? (it becomes lighter) Why does this happen?
(The number of dye molecules becomes diluted ten times
by water in each progression of the serial dilution.)

4.
Does the liquid ever become colorless? (yes). If so,
at what mixing ratios is the liquid colorless? (Answers
will vary depending upon the strength of the initial
solution.) Why do you think it is colorless? (So few
dye molecules are present that they are not visible.)

5.
Which test tube contains one ppm of coloring? (#7) Which
test tube contains one ppb of coloring? (#10)

6.
Ozone in the stratosphere has a mixing ratio in the range
of one to ten ppm. Which containers represent one and
ten ppm? (#7 and #6)

Tell
the students, “You now should be able to visualize
what a concentration of one ppm looks like. Today we
are going to use unit analysis to actually calculate
the parts per million represented by certain ratios.”

Hand
out the Student worksheet, The Numbers Game, and have
the students take the quiz in Part A. The quiz is intended
to gauge the students' intuitive grasp of how small a “part-per-million” and
a “part-per-billion” are. Instruct the students
to guess at the answers of these three questions, not
to do the calculations.

After
the students have completed Part A, go to Part B where
they will calculate each answer choice and, from these
calculations, determine the correct answer to each question
in the quiz.

Finally,
work through the Lake Jasmine spill scenario in Part
C with the students. An answer key to the questions is
provided in the Teacher Background sheets.

Part
A
Just how small is a part per million? A part per billion? Answer
the following three questions based on your “gut reaction.” Guess
if you need to, do not do the calculations.

One part per million is equivalent to 1 minute in

a.
1 day b.
2 years c.
6 weeks

One
part per billion is equivalent to 1 second in

a.
3 weeks b.
17 months c.
32 years

Part
B
Now go back and calculate each of the answers you chose in Part
A. Use the procedure below for each calculation.

To
calculate the relationship between 2 quantities,
use unit analysis to set up your equation. For
example, to compare years and seconds, convert
one year into seconds. To do this, set up ratios
for days per year, then hours per day, minutes
per hour, and finally seconds per minute. The
units will cancel out and you will be left with
the number of seconds per year.

1.
Use the space below to calculate the ratios
representing (a) 1 minute per day, (b) 1 minute
per 2 years, and (c) 1 minute per 6 weeks.
After you have completed each conversion, you
may have to round your answers to the nearest
thousand, million or billion to find the correct
answer to the quiz question.

2.
Use the space below to calculate (a) 1 second
per 3 weeks, (b) 1 second per 17 years, and (c)
1 second per 32 years to find the answer to question
2.

Part
CIf
the conversion of units leads to a
fraction with a numerator other than
1, a different method can be used to
determine parts per million or parts
per billion. Be sure your fraction
has a smaller number on top and larger
number on the bottom and divide.
To express the decimal answer in parts per million, move
the decimal point 6 places to the right. To express the
answer in parts per billion, move the decimal point 9 places
to the right.

Example
1:

Moving
the decimal place 6 places to the right gives
1,250 parts per million.

Moving
the decimal place 9 places to the right gives
1,250,000 parts per billion.
You would probably not see a number this large expressed in parts
per billion. It is better expressed as a smaller number of parts
per million.

Example
2:

Moving
the decimal place 6 places to the right gives
34.37, or about 34.4 parts per million.

Moving
the decimal place 9 places to the right gives
34,370, or about 34,000 parts per billion.

Lake Jasmine is a 20-acre lake
with an average depth of 30 feet. Yesterday afternoon,
four 55-gallon drums of Fuel Oil A and six 55-gallon
drums of Solvent C fell off a truck during an
accident, rolled into lake Jasmine and burst
open on the rocky shore. The entire contents
of all the drums spilled into the lake.

Based on the scenario described
below and the table of legally allowable concentrations
of contaminants in surface water, decide
whether local public health officials should
take measures to keep campers near Lake Jasmine
from using the water.

STEP 1
Calculate the concentration of each contaminant (in ppm) in Lake
Jasmine. To do this you must compare the volume of the contaminants
(gallons) to the volume of the lake (cubic feet). Start by converting
both to cubic feet.

Calculate the volume of the lake:

Water
in Lake Jasmine:

Calculate
volume of contaminants:

Fuel
Oil A:
andSolvent
C:

Comparison
of amounts:

Fuel
Oil A:

Move
the decimal point the appropriate number of places
to the right to calculate the ppm of Fuel Oil
A

Solvent
C:

Move the decimal point the appropriate number of places to the
right to calculate the ppm of Solvent C

STEP 2
Compare these levels to the values in the chart of allowable quantities
to see if they exceed the legally allowable levels.

Assuming
that you are still at Lake Jasmine, which has a volume
of 26,136,000 cubic feet, how many cubic feet of each
of the above toxins could be spilled into the lake before
health officials would need to take action?

Informal
discussion as the students present their models of ppm
will allow you to assess their understanding of how small
a concentration of one ppm truly is. Informal observations
when the students are using unit analysis to calculate
the ppm of a given ratio allows assessment on their understanding
of the procedure they need to follow. Guided practice
and informal observations can be used with the Number
Game to assess how well the students use synthesis to
combine the two ideas to come to a decision of what to
tell the health officials at Lake Jasmine.

PULSE
is a project of the Community Outreach and Education
Program of the Southwest Environmental Health Sciences
Center and is funded by: